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Fuzzy sets have undergone several expansions and generalisations in the literature, including Atanasov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets, to name a few. They can be regarded as fuzzy multisets from a formal standpoint; nevertheless, their interpretation differs from the two other approaches to fuzzy multisets that are currently available. Hesitating fuzzy sets (HFS) are very useful if consultants have hesitation in dealing with group decision-making problems between several possible memberships. However, these possible memberships can be not only crisp values in [0,1], but also interval values during a practical evaluation process. Hesitant bipolar valued fuzzy set (HBVFS) is a generalization of HFS. This paper aims to introduce a general framework of multi-attribute group decision-making using social network. We propose two types of decision-making processes: Type-1 decision-making process and Type-2 decision-making process. In the Type-1 decision-making process, the experts' original opinion is proces for the final ranking of alternatives. In Type-2 decision making processs, there are two major aspects we consider. First, consistency tests and checking of consensus models are given for detecting that the judgments are logically rational. Otherwise, the framework demands (partial) decision-makers to review their assessments. Second, the coherence and consensus of several HBVFSs are established for final ranking of alternatives. The proposed framework is clarified by an example of software packages selection of a university. [ABSTRACT FROM AUTHOR]

In this paper we expose interval rough fuzzy ideals in γ-near-rings. Also we prove some interesting properties of γ-ideal and bi-γ-ideal in γ-nearring. [ABSTRACT FROM AUTHOR]

This paper expose a study on rough interval valued pythagorean fuzzy sets in semigroups. We characterize rough interval valued pythagorean fuzzy sets by an exam- ple. Characterize composition of two interval valued pythagorean fuzzy sets. Introduce rough interval valued pythagorean fuzzy left(right, bi-, interior-,(1,2)-)ideals in semi- groups. Moreover we prove an interval valued pythagorean fuzzy set is an upper rough interval valued pythagorean fuzzy left(right) ideal of semigroup also we give an example for converse of this is not true. Lower and upper approximation of an interval valued pythagorean fuzzy ideal of semigroup is an interval valued pythagorean fuzzy ideal of semigroup. [ABSTRACT FROM AUTHOR]

Brain tumor segmentation is a significant task in screening and treating brain diseases. However, this process is quite formidable due to the inhomogeneous characteristics of tumors. Thus, it is indeed to ameliorate the preciseness of tumor segmentation for the diagnostic process. From this perspective, this work intends to develop an algorithm to segment the brain images, which augments the certainty of the outcome with curtailed computational complexity. As a foremost process, a novel intuitionistic fuzzy generator (IFG) is constructed to enhance the contrast of the ill-illumined source brain images by reducing the vagueness in the clinical images. Following this, the enhanced medical image is morphologically reconstructed to preserve the details in the source images. Then, the histogram is computed on the reconstructed image, and it is clustered by formulating the novel clustering algorithm called effective intuitionistic fuzzy c-means clustering (EIFCM) to procure the segmented result. Finally, the segmented outcome is evaluated against four other state-of-the-art methods, and the results are presented and discussed in both the qualitative and quantitative aspects, which delineate the potency of the proposed algorithm. • A new generator is derived to enhance contrast and remove vagueness in brain images. • A novel clustering algorithm based on histogram is derived to reduce computational cost. • Efficacy of the proposed algorithm is validated in objective and subjective aspects. [ABSTRACT FROM AUTHOR]

• Two scale decomposition helps to extract the significant features of the image. • Sugeno intutionistic fuzzy set effectively eradicates the uncertainty in the images. • The proposed fusion algorithm provides the enhanced fusion result of grayscale medical images with good contrast and high structural information. • The objective and subjective assessment shows the proposed fusion algorithm is superior than other methods. The main aim of this paper is to blend the multi-modality images into a single image to acquire superior information and obtain excellent visual quality without any artifacts and vagueness. First, the source images are decomposed into base and detail layers by making use of the Gaussian filter. The detail layers are merged using spatial frequency to preserve the edge details and clarity of an image. Due to the reason that the base layer contains approximate information of source image with low contrast, it is transformed into Sugeno's intuitionistic fuzzy image (SIFI). Texture information is extracted from SIFI to fuse the base layers. Finally, the fused output image with enhanced contrast and better visual effects is reconstructed by integrating both the fused base and fused detail layer. Furthermore, the experimental results demonstrate the efficacy of the proposed method over other fusion methods. Both subjective and objective assessment illustrates that the proposed method presents a fused output image that has good visual quality with enhanced contrast and no artifacts included. [ABSTRACT FROM AUTHOR]